A319054 Maximum product of an aperiodic integer partition of n.

1, 2, 3, 4, 6, 8, 12, 18, 24, 36, 54, 72, 108, 162, 216, 324, 486, 648, 972, 1458, 1944, 2916, 4374, 5832, 8748, 13122, 17496, 26244, 39366, 52488, 78732, 118098, 157464, 236196, 354294, 472392, 708588, 1062882, 1417176, 2125764, 3188646, 4251528, 6377292

Offset: 1

Author

Gus Wiseman, Sep 09 2018

Keywords

• nonn

Comments

An integer partition is aperiodic if its multiplicities are relatively prime.

Examples

			Among the aperiodic partitions of 9, those with maximum product are (432) and (3222), so a(9) = 24. If periodic partitions were allowed, we would have (333) with product 27.
		

Crossrefs

Cf. A000740, A000792, A000793, A000837, A007916, A100953, A281116, A289508, A289509, A296302.

Programs

Mathematica

Table[Max[Times@@@Select[IntegerPartitions[n],GCD@@Length/@Split[#]==1&]],{n,30}]